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Regular pairs of quadratic forms on odd-dimensional spaces in characteristic 2. (English) Zbl 1485.11074

Summary: We describe a normal form for a smooth intersection of two quadrics in even-dimensional projective spaces over an arbitrary field of characteristic 2. We use this to obtain a description of the automorphism group of such a variety. As an application, we show that every quartic del Pezzo surface over a perfect field of characteristic 2 has a canonical rational point and, thus, is unirational.

MSC:

11E04 Quadratic forms over general fields
14C21 Pencils, nets, webs in algebraic geometry
14G17 Positive characteristic ground fields in algebraic geometry
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